“That is something that we are pleased to do because Canada is a country that understands how important it is to stand up for human rights and to stand up for woman’s rights around the world,” Mr Trudeau said.
“I can confirm that we have accepted the UN’s request.”
Ms al-Qunun was stopped last Saturday in Thailand, when immigration police seized her passport and refused her entry.
She barricaded herself in an airport hotel room and launched a social media campaign, drawing global attention to her desperate pleas for asylum.
The teenager said that she escaped during a trip to Kuwait and that her life would be in danger if she was forced to return to her family in Saudi Arabia.
The viral campaign caused Thai officials to temporarily admit the teenager to the county, under the protection of UN officials.
The UN High Commissioner for Refugees granted Ms al-Qunun refugee status on Wednesday.
“She chose Canada. It’s her personal decision,” Thailand police chief Surachate Hakparn said, adding that Ms al-Qunun thanked everyone who had helped her.
“She still refuses to meet with her father and brother, and they are going to be travelling back tonight as well ... They are disappointed,” he said.
The teenager’s case has once again highlighted the lives of women in Saudi Arabia, a deeply conservative country where they have limited rights.
Several Saudi women attempting to flee abuse from their families have been caught and returned home.
Canada’s decision to offer Ms al-Qunun asylum could further damage the country’s links with Saudi Arabia.
Relations between the countries have deteriorated after Canada’s Foreign Ministry tweeted support for women’s right activists arrested in the kingdom.
In response Saudi Arabia expelled Canada’s ambassador to the kingdom and sold Canadian investments.
Additional reporting by agencies